{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "usDG-zMJWI20"
   },
   "source": [
    "# 一个完整的scipy.optimize.minimize训练例子\n",
    "\n",
    "测试用python版本为3.6\n",
    "* 机器学习路径：https://github.com/loveunk/machine-learning-deep-learning-notes/\n",
    "* 内容正文综合参考网络资源，使用中如果有疑问请联络：www.kaikai.ai"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import optimize\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\" X是训练集的数据 \"\"\"\n",
    "X_train = np.array([[1.,  1.],\n",
    "              [1.,  2.],\n",
    "              [-1., -1.],\n",
    "              [-1., -2.]])\n",
    "\"\"\" y是训练集的label \"\"\"\n",
    "y_train = np.array([1, 1, 0, 0])\n",
    "\n",
    "\"\"\" 处理训练集X，补上x_0 \"\"\"\n",
    "X_train = np.hstack((np.ones((X_train.shape[0], 1)), X_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"Sigmoid 函数公式 \"\"\"\n",
    "def sigmoid(z):\n",
    "  return 1/(1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\" 目标函数，也就是待最小化的 Cost function \"\"\"\n",
    "def cost(theta, X, y):\n",
    "  first = - y.T @ np.log(sigmoid(X @ theta))\n",
    "  second = (1 - y.T) @ np.log(1 - sigmoid(X @ theta))\n",
    "  return ((first - second) / (len(X))).item()\n",
    "\n",
    "def hypothesis(X, theta):\n",
    "  return sigmoid(X @ theta)\n",
    "\n",
    "def cost_wrapper(theta):\n",
    "  return cost(theta, X_train, y_train)\n",
    "\n",
    "def hypothesis_wrapper(theta):\n",
    "  return hypothesis(X_train, theta)\n",
    "\n",
    "\"\"\" 目标函数的梯度 \"\"\"\n",
    "def gradient(theta):\n",
    "  ret = (1/X_train.shape[0])*((hypothesis_wrapper(theta) - y_train).T @ X_train)\n",
    "  return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     fun: 7.91774566928816e-06\n",
      "     jac: array([ 2.15714436e-08, -7.91768325e-06, -7.93516986e-06])\n",
      " message: 'Optimization terminated successfully.'\n",
      "    nfev: 34\n",
      "     nit: 6\n",
      "    njev: 34\n",
      "  status: 0\n",
      " success: True\n",
      "       x: array([2.72451378e-03, 4.94223996e+00, 6.11322367e+00])\n"
     ]
    }
   ],
   "source": [
    "theta_train = np.array([1, 1.,2.])\n",
    "\n",
    "theta_opt = optimize.minimize(cost_wrapper, theta_train, method='CG', jac=gradient)\n",
    "print(theta_opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 494
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2905,
     "status": "ok",
     "timestamp": 1551364998036,
     "user": {
      "displayName": "Wen QI",
      "photoUrl": "https://lh4.googleusercontent.com/-JqeVAdmmxc8/AAAAAAAAAAI/AAAAAAAAFLU/8N8KzOraE6M/s64/photo.jpg",
      "userId": "17732479532480119355"
     },
     "user_tz": -480
    },
    "id": "r3GaSVl9-TO5",
    "outputId": "7eb67a1f-bb1a-4760-ca66-08749ba58cce"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\" 构造预测集数据 \"\"\"\n",
    "delta = 0.2\n",
    "px = np.arange(-3.0, 3.0, delta)\n",
    "py = np.arange(-3.0, 3.0, delta)\n",
    "px, py = np.meshgrid(px, py)\n",
    "px = px.reshape((px.size, 1))\n",
    "py = py.reshape((py.size, 1))\n",
    "pz = np.hstack((np.hstack((np.ones((px.size, 1)), px)), py))\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(X_train[:, 1], X_train[:, 2], y_train, color='red', marker='^', s=200, label='Traning Data')  # plot训练集\n",
    "ax.scatter(px, py, (hypothesis(pz, theta_opt.x)), color='gray', label='Prediction Data')  # plot预测集, 分类时加上 np.around\n",
    "ax.legend(loc=2)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('z')\n",
    "ax.set_title('classification')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "logistic_regression_sample_with_optimize.minimize.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python (Python 3.6)",
   "language": "python",
   "name": "python36"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
